I would argue that those two sentences have slightly different meanings. Going down the stairs describes the act of using a staircase to descend somewhere. Going downstairs just means that you went to a lower floor, and doesn't specify how you got there. The Japanese sentence specifically references going down a set of stairs.

"Downstairs" is a place. You can go downstairs in an elevator, but おりる means to descend something, so you can't エレベーターをおりました, because you can't descend an elevator. You can, however, descend IN an elevator, but I'm not sure if you can do so in Japanese...